The StarHex-II tiles consist of all the shapes of one, two or three hexagons with one, two or three triangles attached. They can be overlaid on a tiling of stars. Happily, that produces 17 pieces with just the right proportion of hexagons to triangles that they can form concave-bordered symmetrical shapes. Below is a sampling from the booklet:

The diagrams below show that solutions exist for every possible position of the "triplehex" piece within the tray:

You can also fill the tray with the full gamut of having each color grouped and each color separated. The latter was arguably the most difficult to find (shown on previous page). That solution is by Kate Jones. We will send a prize to finders of any new solution where no two of the same color touch except at corner points!